Angular Momentum

Of a Bicycle Wheel We will begin our discussion of the angular momentum of a bicycle wheel using the picture of a bicycle wheel, i.e., a collection of balls on the end of massless rods or spokes. If the wheel is rotating with an angular velocity ω , then each ball has a tangential velocity vt given by Equation 1

v_t = rω (1)
If the i-th ball in the wheel (identified in Figure 1) has a mass m_i , then its angular momentum will be given by

............(2)

Assuming that the total angular momentum L of the bicycle wheel is the sum of the angular momenta of each ball (we will discuss this assumption in more detail shortly) we get

............(3)

Since each mass m_i is at the same radius r and is traveling with the same angular velocity ω , we get

Noting that M = (Σ_i m_i) is the total mass of the bicycle wheel, we get

............(4)

Figure 1: The angular momentum of the i’th ball is m_i v_tr_i .